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Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players.
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Yves Achdou, Fabio Camilli, and Italo Capuzzo-Dolcetta, Mean field games: numerical methods for the planning problem , SIAM J. Control Optim. 50
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Yves Achdou, Finite difference methods for mean field games , Hamilton-Jacobi equations: approximations, numerical analysis and applications, Lecture Notes in Math., vol. 2074, Springer, Heidelberg, 2013, pp. 1–47. MR 3135339
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by same author, Mean field games: convergence of a finite difference method , SIAM J. Numer. Anal. 51
2013
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Alain Bensoussan, Jens Frehse, and Sheung Chi Phillip Yam, Mean field games and mean field type control theory , Springer Briefs in Mathematics, Springer, New York, 2013
2013
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Pierre Cardaliaguet, Notes on mean field games , 2013
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Elisabetta Carlini and Francisco J. Silva, A fully discrete semi-Lagrangian scheme for a first order mean field game problem , SIAM J. Numer. Anal. 52
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Diogo A. Gomes and João Saúde, Mean field games models—a brief survey , Dyn. Games Appl. 4
2014
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Mathieu Laurière and Olivier Pironneau, Dynamic programming for mean-field type control , C. R. Math. Acad. Sci. Paris 352
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Yves Achdou and Mathieu Laurière, On the system of partial differential equations arising in mean field type control , Discrete Contin. Dyn. Syst. 35
2015
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Jean-David Benamou and Guillaume Carlier, Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations , J. Optim. Theory Appl. 167
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Pierre Cardaliaguet, P. Jameson Graber, Alessio Porretta, and Daniela Tonon, Second order mean field games with degenerate diffusion and local coupling , NoDEA Nonlinear Differential Equations Appl. 22
2015
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by same author, A semi-Lagrangian scheme for a degenerate second order mean field game system , Discrete Contin. Dyn. Syst. 35
2015
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René Carmona and François Delarue, Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics , Ann. Probab. 43
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Alpár Richárd Mészáros and Francisco J. Silva, A variational approach to second order mean field games with density constraints: the stationary case , J. Math. Pures Appl. (9) 104
2015
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Yves Achdou and Mathieu Laurière, Mean Field Type Control with Congestion , Appl. Math. Optim. 73
2016
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by same author, Mean Field Type Control with Congestion (II): An augmented Lagrangian method , Appl. Math. Optim. 74
2016
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Yves Achdou and Alessio Porretta, Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games , SIAM J. Numer. Anal. 54
2016
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Pierre Cardaliaguet, Alpár R. Mészáros, and Filippo Santambrogio, First order mean field games with density constraints: pressure equals price , SIAM J. Control Optim. 54
2016
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Diogo A. Gomes, Edgard A. Pimentel, and Vardan Voskanyan, Regularity theory for mean-field game systems , SpringerBriefs in Mathematics, Springer, [Cham], 2016. MR 3559742
2016
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2019
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2019
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2019
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Alekos Cecchin, Paolo Dai Pra, Markus Fischer, and Guglielmo Pelino, On the convergence problem in mean field games: a two state model without uniqueness , SIAM J. Control Optim. 57
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2016
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Vassili N. Kolokoltsov and Alain Bensoussan, Mean-field-game model for botnet defense in cyber-security , Appl. Math. Optim. 74
2016
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by same author, Dynamic programming for mean-field type control , J. Optim. Theory Appl. 169
2016
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Laurent Pfeiffer, Numerical methods for mean-field type optimal control problems , Pure Appl. Funct. Anal. 1
2016
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Noha Almulla, Rita Ferreira, and Diogo Gomes, Two numerical approaches to stationary mean-field games , Dyn. Games Appl. 7
2017
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Roman Andreev, Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion , SIAM J. Sci. Comput. 39
2017
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Jean-David Benamou, Guillaume Carlier, and Filippo Santambrogio, Variational mean field games , Active particles. Vol. 1. Advances in theory, models, and applications, Model. Simul. Sci. Eng. Technol., Birkhäuser/Springer, Cham, 2017, pp. 141–171. MR 3644590
2017
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Simone Cacace, Fabio Camilli, and Claudio Marchi, A numerical method for mean field games on networks , ESAIM Math. Model. Numer. Anal. 51
2017
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Jean-François Chassagneux, Dan Crisan, and François Delarue, Numerical method for FBSDEs of McKean-Vlasov type , Ann. Appl. Probab. 29
2019
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2019
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2019
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2019
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2019
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Xin Guo, Anran Hu, Renyuan Xu, and Junzi Zhang, Learning mean-field games , in proc. of NeurIPS, 2019
2019
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Saeed Hadikhanloo and Francisco J. Silva, Finite mean field games: fictitious play and convergence to a first order continuous mean field game , J. Math. Pures Appl. (9) 132
2019
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2019
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Levon Nurbekyan et al., Fourier approximation methods for first-order nonlocal mean-field games , Portugaliae Mathematica 75
2019
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Jayakumar Subramanian and Aditya Mahajan, Reinforcement learning in stationary mean-field games , in proc. of AAMAS, 2019
2019
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2020
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by same author, Mean field games and applications: Numerical aspects , Mean Field Games, C.I.M.E. Foundation Subseries, vol. 2281, Springer International Publishing, 2020
2020
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Yves Achdou, Mathieu Laurière, and Pierre-Louis Lions, Optimal control of conditioned processes with feedback controls , Journal de Mathématiques Pures et Appliquées (2020)
2020
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Nacira Agram, Azzeddine Bakdi, and Bernt Oksendal, Deep learning and stochastic mean-field control for a neural network model , Available at SSRN 3639022 (2020)
2020
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2020
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2020
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2020
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2020
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François Delarue, Master equation and mean field games , Proc. AMS Short Course (2020)
2020
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François Delarue, Daniel Lacker, and Kavita Ramanan, From the master equation to mean field game limit theory: large deviations and concentration of measure , Ann. Probab. 48
2020
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Romuald Elie, Julien Pérolat, Mathieu Laurière, Matthieu Geist, and Olivier Pietquin, On the convergence of model free learning in mean field games , AAAI, 2020
2020
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Jean-Pierre Fouque and Zhaoyu Zhang, Deep learning methods for mean field control problems with delay , Frontiers in Applied Mathematics and Statistics 6(11)
2020
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Christy Graves and Roland P. Malhamé, Mean field games : A paradigm for individual-mass interactions , Proc. AMS Short Course (2020)
2020
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2020
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Daniel Lacker, Notes for the AMS short course on mean field games: The convergence problem , Proc. AMS Short Course (2020)
2020
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Rajesh K Mishra, Deepanshu Vasal, and Sriram Vishwanath, Model-free reinforcement learning for non-stationary mean field games , 2020 59th IEEE Conference on Decision and Control (CDC), IEEE, 2020, pp. 1032–1037
2020
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Marcel Nutz and Yuchong Zhang, Conditional optimal stopping: a time-inconsistent optimization , Ann. Appl. Probab. 30
2020
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Sarah Perrin, Julien Pérolat, Mathieu Laurière, Matthieu Geist, Romuald Elie, and Olivier Pietquin, Fictitious play for mean field games: Continuous time analysis and applications , in proc. of NeurIPS, 2020
2020
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Kavita Ramanan, Deviations and fluctuations for mean field games , Proc. AMS Short Course (2020)
2020
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Lars Ruthotto, Stanley J Osher, Wuchen Li, Levon Nurbekyan, and Samy Wu Fung, A machine learning framework for solving high-dimensional mean field game and mean field control problems , Proceedings of the National Academy of Sciences 117
2020
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by same author, Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games: I–the ergodic case , To appear in SIAM Journal on Numerical Analysis (2021)
2021
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by same author, On the interpretation of the Master Equation , Stochastic Process. Appl. 127
2093
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